Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is pre...
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Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously, differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive.
Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods...
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Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrained optimization can be expressed as similar systems of linear equations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.
Deconvolution problem is a main topic in signal processing. Many practical applications are re-quired to solve deconvolution problems. An important example is image reconstruction. Usually, researcherslike to use regu...
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Deconvolution problem is a main topic in signal processing. Many practical applications are re-quired to solve deconvolution problems. An important example is image reconstruction. Usually, researcherslike to use regularization method to deal with this problem. But the cost of computation is high due to thefact that direct methods are used. This paper develops a trust region-cg method, a kind of iterative methodsto solve this kind of problem. The regularity of the method is proved. Based on the special structure of thediscrete matrix, FFT can be used for calculation. Hence combining trust region-cg method with FFT is suitablefor solving large scale problems in signal processing.
Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are give...
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Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the i...
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The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.
The symmetric Sinc-Galerkin method applied to a sparable second-order self-adjoint elliptic boundary value problem gives rise to a system of linear equations(Ψx⊗Dy+Dx⊗Ψ y)u=g,where⊗ is the Kronecker product symbol, ...
Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor syste...
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Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor system. Description of the tested problems and computing environment used in the computations; Description of the asynchronous multisplitting unsymmetric accelerated overrelaxation method; Discussion of results.
作者：
KANGTong(康彤)YUDe-hao(余德浩)State Key Laboratory of Scientific and Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100080 P R China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100080 P R China
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...
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A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative...
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Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative algorithm is presented. The convergence of this iterative algorithm is proved, and then the efficiency of the algorithm is tested by a numerical example.
Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of n...
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Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.
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